General method of geometrical passive ranging

ABSTRACT

1. A passive ranging system for use by a fighter in determining the  dista along the line of sight between the fighter and a target travelling at constant speed; comprising in combination: a search and track system operable to generate signals proportional to the azimuth and elevation angles of the line of sight with respect to the fighter coordinate system, a stabilized platform normally slaved to said search and track system operable to generate signals proportional to the angular rate of rotation of the line of sight and signals proportional to the acceleration of the fighter in inertial space, resolver computer means coupled to said stabilized platform operable to resolve said angular rate and acceleration signals into terms of a reference coordinate system, algebraic computer means connected to said stabilized platform and said resolver computer operable to transform said signals into a voltage form representative of range between the fighter and the target.

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

This invention relates to a system for determining the distance betweentwo points in space and more particularly to a passive ranging systemfor determining the range between a fighter and a target.

Range determining techniques are essential with the advent of moreadvanced armament control systems employing missiles, since it is ofparamount importance to determine whether the distance from theinterceptor to the target at the time of missile launching is within theaerodynamic range of a missile. Range information is also necessarybecause it enables the pilot to determine the moment at which he mustleave the collision path to avoid colliding with the debris of thetarget.

It is well known that the most accurate methods for determining rangebetween a target and interceptor makes use of techniques employingradar. In employing this method, the interceptor fighter emits orradiates microwave energy which is reflected back by the target and thetime between initial radiation and receipt of the reflected waveprovides an accurate measure of the range to the target. A disadvantageof this method lies in the fact that the interceptor utilizing activetechniques to determine range may give his presence away. An enemytarget may be employing countermeasure techniques which enable it todefeat the microwave radiation from the interceptor.

In determining range using passive ranging techniques the interceptorrelies solely on the radiation emitted by the target to calculate rangeand thereby the possibility that the presence of the interceptor will bedetected by the target is greatly reduced since no active radiationemanates from the interceptor itself.

Because of the importance of passive range measuring, many suchtechniques are presently under investigation. The majority of thesetechniques fall into one of three categories: trigonometric, optical,and maneuver (geometric) range finding.

The trigonometric range finding technique employs a pair of radiationdetectors carried on the fighter which define one side of a triangle.The distance between target and interceptor defines another side of thetriangle and is the range. This technique enables the computer to effectan instantaneous solution of a plane triangle with one side and twoangles given or known.

Optical range finding techniques make use of simple optical laws todevelop the relationship between the intensity of target radiation andthe range to the target.

Maneuver techniques are based on the parameters which may be obtainedfrom the relationship of the absolute motion of the interceptor and therelative motion of the target. These techniques derive range from thesolutions of the vector equations which relate range, interceptorvelocity, target velocity, bearing angle, their time derivatives andtime integrals. In order to gather all the parameters necessary for thesolution of the ranging equation, the interceptor may carry on certainprescribed maneuvers. For example, in one maneuver type technique theinterceptor is required to fly in and then deviate from a plane definedby the line of sight and the target velocity vector. A second methodrequires the fighter to first position itself on a collision course andthen deviate from the course while remaining in the kinematic plane,which is the plane defined by the line of sight and target velocityvectors. Both of these methods require specific maneuvers of theinterceptor because they employ two dimensional geometrical techniques.

The present invention contemplates a ranging technique which involvesthree dimensional mathematics wherein the range vector represents thedistance from the interceptor to the target directed along the line ofsight. While a fighter or interceptor is normally maneuvering intoposition for an attack against a nonmaneuvering target, it is possiblefrom observation and measurement of the angular motion of the line ofsight between the fighter and the target, and its time derivatives, andthe fighter's own motion relative to either inertial or air mass spaceto determine all the parameters necessary for the solution of the rangeequation which will be derived hereinbelow. Thus, this inventioneliminates the necessity of a fighter or interceptor going through acertain prescribed or preset pattern of maneuvers in order to obtain theparameters necessary for the solution of a range equation.

Therefore it is an object of the present invention to provide a systemcapable of being incorporated into the fire control system of a moderninterceptor or fighter which will compute distance between a target andthe fighter, utilizing radiation emitted from the target.

It is another object of the present invention to provide a passiveranging system which eliminates course and maneuver restrictions on thefighter and which by measuring angular and angular rate changes both inand perpendicular to the initial kinematic plane receives sufficientinformation to determine distance between fighter and target.

Yet another object of the present invention is to provide a generalmethod of geometrical passive ranging from which range information isobtained instantaneously and continually.

With these and other objects in view, as will hereinafter more fullyappear, and which will be more particularly pointed out in the appendedclaims, reference is now made to the following description taken inconnection with the accompanying drawings in which:

FIG. 1 represents in three dimensions the geometrical relationshipbetween a target and a fighter.

FIG. 2 shows a block diagram representation of the generalinstrumentation of the range equation incorporated in the fire controlsystem of an aircraft.

FIG. 3 illustrates in block diagram form the preferred embodiment ofthis invention.

FIG. 4 is a detailed representation of the resolver computer of FIG. 3.

FIG. 5 is a detailed representation of the algebraic computer of FIG. 3.

FIG. 6 is a schematic illustration of the resolvers used in the resolvercomputer of FIG. 4.

For convenience in understanding and presenting the concept behind thisinvention, the physical relationships between a fighter and the targetin three dimensional space, as best illustrated by FIG. 1, will now bediscussed. These physical relationships are discussed with the view ofultimately obtaining the necessary parameters for derivation of therange equation. Once the physical relationship is set up and the rangeequation derived, the instrumentation for obtaining the necessaryparameters and for the solution of the range equation will be discussed.

FIG. 1 shows a fighter and a target in three dimensional space which isrepresented by the vector coordinate system i_(o) j_(o) k_(o). The k_(o)axis is parallel to the direction of gravitational force. At a time t =0, the fighter and target are in the positions shown. The distancebetween them is the vector R_(o) at time t = 0. The angle between theplane defined by i_(o) and j_(o) and the range vector R_(o) is α_(o).After a time t, the fighter has moved a distance represented by thevector V_(f) dt and the target has moved a distance represented by thevector V_(t) dt. The distance between the fighter and the target at timet is represented by the vector R_(t). The angle between the respectivehorizontal projections in the i, j plane of the range vector at time t =0 and at time t is represented by angle σ_(t). The angle between the newline of sight R_(t) and the plane defined by the i_(t) and j_(t) vectorsis represented by α_(t).

Definition of Coordinate System

Consider an orthogonal, three dimensional, right-handed, unit vectorcoordinate system i_(t) j_(t) k_(t), to be defined by any twononcoincident vectors, a_(t) and b_(t) intersecting at a common originF. In general a_(t) and b_(t) are functions of time, and the origin F isbeing translated with a velocity V_(Ft) relative to some inertialreference origin O. Further the vectors a_(t) and b_(t) may be rotatingin space, so that the resultant coordinate system i_(t) j_(t) k_(t) isrotating with a rate ω_(t) relative to inertial space.

The coordinate system used in deriving the range equation of the presentinvention is defined below:

    i.sub.t = j.sub.t ×  k.sub.t                         (1) ##EQU1## where θ.sub.t is the angle between a.sub.t and b.sub.t

X represents a vector cross product.

General Geometric Relationships

Consider a point T moving with a velocity R_(t) relative to the origin Fof the i_(t) j_(t) k_(t) coordinate system at a vector distance R_(t)from the origin F. Any velocity V_(T).sbsb.t that point T has relativeto a fixed reference 0 must be the vector sum of R_(t) and the velocityV_(F).sbsb.t of F relative to the 0 reference so that

    V.sub.T.sbsb.t = R.sub.t + V.sub.F.sbsb.t or R.sub.t = V.sub.T.sbsb.t - V.sub.F.sbsb.t                                            (4)

r_(t) - R_(o) is the integral of R_(t) from time t_(O) to time t:##EQU2##

Since the coordinate i_(t) j_(t) k_(t) will in general be rotating witha rate ω_(t), the effect of this rotation upon the parameters involvedmust necessarily be considered.

    ω.sub.t = i.sub.t (ω.sub.i).sub.t + j.sub.t (ω.sub.j).sub.t + + k (ω.sub.k).sub.t         (6)

As the above equation states ω_(t) is made up of the three components ofrotation about the individual coordinate axes i_(t) j_(t) k_(t).

It is known that the time rate of change of each unit vector equals thecross product of total rotation rate ω_(t) with each respective vector:

    i.sub.t = ω.sub.t × i.sub.t = (ω.sub.k) j.sub.t - (ω.sub.j).sub.t k.sub.t                             (7)

    j = ω.sub.t × j.sub.t = (ω.sub.i).sub.t k.sub.t - (ω.sub.k).sub.t i.sub.t                             (8)

    k = ω.sub.t × k.sub.t = (ω.sub.j).sub.t i.sub.t - (ω.sub.i).sub.t j.sub.t                             (9)

For a gravity-dependent system, a_(t) = g_(t), b_(t) = R_(t), and θ_(t)= 90° - α_(t),

where

g_(t) is the gravity vector

α_(t) is the angle of elevation of the line of sight at time t.

R_(t) is the range vector and is the desired quantity.

Therefore, the coordinate system to be used in the derivation of R_(t)is defined by:

    k.sub.t = gt/gt                                            (10)

    j.sub.t = (k.sub.t × R.sub.t)/(R.sub.t cos α.sub.t) (11)

    i.sub.t = j.sub.t × k.sub.t                          (12)

from equation (11)

    j.sub.t R.sub.t cos α.sub.t = k.sub.t × R.sub.t

Since

    i.sub.t = j.sub.t × k.sub.t                          (13)

    i.sub.t |R.sub.t |cos α.sub.t = j.sub.t × k.sub.t |R.sub.t |cos α.sub.t = (k.sub.t × R.sub.t) × k.sub.t

But

    (k.sub.t × R.sub.t) × k.sub.t = R.sub.t + k.sub.t |R.sub.t |sin α.sub.t

Therefore

    R.sub.t = i.sub.t |R.sub.t |cos α.sub.t - k.sub.t |R.sub.t |sin α.sub.t             (14)

and substituting from equation (4), noting R_(t) = |R_(t) |:

    R.sub.t = (V.sub.T.sbsb.t - V.sub.F.sbsb.t) = i.sub.t R.sub.t cos α.sub.t + i.sub.t R.sub.t cos α.sub.t - i.sub.t R.sub.t α.sub.t sin α.sub.t - k.sub.t R.sub.t sin α.sub.t - k.sub.t R.sub.t sin α.sub.t - k.sub.t R.sub.t α.sub.t cos α.sub.t                                             (15)

from equation (15); taking components along i_(t), j_(t) and k_(t) :

    (V.sub.T.sbsb.t - V.sub.F.sbsb.t).sup.. i.sub.t = R.sub.t cos α.sub.t - R.sub.t α.sub.t sin α.sub.t - R.sub.t (ω.sub.j).sub.t sin α.sub.t                                         (16)

    (V.sub.T.sbsb.t a - V.sub.F.sbsb.t).sup.. j.sub.t = R.sub.t (ω.sub.k).sub.t cos α.sub.t + R.sub.t (ω.sub.i).sub.t sin α.sub.t                                         (17)

    (V.sub.T.sbsb.t - V.sub.F.sbsb.t).sup.. k.sub.t = -R.sub.t (ω.sub.j).sub.t cos α.sub.t - R.sub.t sin α.sub.t - R.sub.t α.sub.t cos α.sub.t                   (18)

and from equation (5) ##EQU3##

Since the velocity at time t may be considered in terms of velocity attime t_(o) and the integral of the acceleration from time t_(o) to t.##EQU4##

Substituting from equations 16, 17, and 18 with t = t_(o) into equations19, 20, and 21, we have, noting that ##EQU5## For the physicalconditions we are investigating, i.e. nonmaneuvering target, and asufficiently short time interval such that g remains constant,V_(T).sbsb.t = 0; (ω_(i))_(t) = (ω_(j))_(t) = 0. Also, we noteR_(o).i_(o) = R_(o) cos α_(o), R_(o).sup.. j_(o) = 0, R_(o).sup.. k_(o)= -R_(o) sin α_(o) ; and for consistency call (ω_(k))_(o) = σ_(o) :##EQU6## Multiplying equation 27 by sin α_(o) and adding to it equation29 multiplied by cos α_(o), we have (eliminating R_(o)) ##EQU7## andsubstituting R_(o) t from equation 28 into equation 30 we have: ##EQU8##and

    R.sub.t.sup.. j.sub.o = R.sub.t cos α.sub.t sin σ.sub.t (32)

    R.sub.t.sup.. i.sub.o = R.sub.t cos α.sub.t cos σ.sub.t (33)

    R.sub.t.sup.. k.sub.o = -R.sub.t sin α.sub.t         (34)

which is the range vector R_(t) resolved on the i_(o) j_(o) k_(o) axes.

Rationalizing and expanding: ##EQU9## and collecting terms in R_(t) :##EQU10##

Instrumentation

FIG. 2 illustrates in block diagram form the passive ranging system ofthis invention incorporated in the fire control system of a modernfighter aircraft. The search and track system 21, which is sensitive toradiation emitted by a body, such as an enemy aircraft, is of the typegenerally carried by many fighter aircraft. It generates azimuth andelevation angle signals and angular rate signals which are fed through asmoother 24 to a switch 26. A stabilized platform 23 may be of the fourgimbal type commonly used in fighter aircraft for navigation purposes.The stabilized platform 23 is normally slaved to the search and tracksystem. In the track mode, the search and track system 21 suppliesvoltages representing the angles of elevation and azimuth (E_(l) andA_(z)) of the antenna relative to the aircraft. Two of the four platformgimbals are torqued to align the R axis in space. Two of the platformgimbals maintain the inner platform as a gravity reference. The platformis then tracking the line of sight to the target and determining the i jk axes. Stabilized platform 23, by virtue of j and k axes gyros,generates signals proportional to α and σ which are the firstderivatives of the general angles defined in connection with FIG. 1. Thestabilized platform also has linear accelerometers along each of the i jk axes.

The passive ranging system 22 can operate in two different modes whichdepend on the coordinate reference system chosen. In one case(continuous tracking) the signals proportional to accelerations from thestabilized platform must be resolved in terms of the i j k axes. Thesignals α and σ from the gyros do not need to be resolved since each ismeasured directly because the gyros are coincident with the i j kreference system at the time of measurement.

The second mode of operation is called the Freed Platform type in whichat time t = 0 the platform is stabilized to maintain the i_(o) j_(o)k_(o) axes in space. The accelerometers along these axes in the platformsupply fighter acceleration components directly. However, resolvers arenecessary to determine the required trigonometric functions of α_(t) andσ_(t) in terms of the i_(o) j_(o) k_(o) coordinate reference system.

In short, in the first case the stabilized platform 23 gives the α_(t)and σ_(t) information directly while the acceleration components of theaircraft must be resolved. In the second case the stabilized platform 23gives the acceleration components directly while the angular informationmust be resolved.

Continuing with the description of FIG. 2, all of the signals fromstabilized platform 23 are fed into resolver and computer 27, theresolver part of which resolves either the acceleration components orthe angles depending upon in which mode it is desired to operate theranging system. The computer part of resolver and computer 27 solves therange equation 36 to give a signal proportional to R which may be fedinto display 28 for immediate indication of the range.

The second mode of operation of the passive ranging system is thepreferred embodiment of this invention and is more fully described inconnection with FIGS. 3, 4 and 5.

FIG. 3 illustrates the manner in which the range equation is mechanized.Reference numeral 21 represents a conventional search and track antennasystem of the type that seeks out and tracks a target normally emittingany type of radiations. As a result of tracking the target, the searchand track system generates two angles, A_(z) and E_(l). A_(z) is theazimuth angle of the line of sight from the antenna to the target. E_(l)is the elevation angle of the line of sight from the antenna to thetarget.

Reference numeral 23 represents a stabilized platform of the typecarried by many modern military aircraft. It is capable of developingsignals proportional to the four angles which are here defined as

θ = platform azimuth angle

φ = platform elevation (outer pitch) angle

γ = platform roll angle

α_(g) = platform inner pitch angle

The platform is also capable of producing signals proportional to thecomponents of fighter acceleration along the coordinate system axesdefined by the stabilized platform.

The signals representing azimuth and elevation A_(z) and E_(l) are fedfrom the search and track system via conductors 31, 32, switch box 29and conductors 33 and 34 as shown in FIG. 3. The stabilized platform isslaved to the search and track system and during the tracking intervalbefore time, t = 0

    A.sub.z = θ and E.sub.l = φ

while γ and α_(g) are determined by the relative position of the line ofsight and the gravity vector.

The stabilized platform contains rate gyro for each of the generalcoordinate axes i j k which generate signals proportional to α, α and σwhere σ is in general the rate of rotation about the k axis and α is therotation rate about the j axis.

At a certain time, t = 0, the switch box is operated to disconnect thesignals representing A_(z) and E_(l) from the stabilized platform whichis consequently freed to become a free space stabilized platformdefining an inertial reference coordinate system i_(o) j_(o) k_(o) withthe one condition that the k_(o) axis as shown in FIG. 1 is parallelwith the gravity vector g.

At this time t = 0, A_(z) = θ, E_(l) = φ, and the angles θ, φ, γ andα_(g) are representative only of fighter rotation about the stabilizedplatform. The azimuth and elevation angles are representative only ofthe rotation of the line of sight or range vector R about the origin ofthe x y z coordinate system of the aircraft.

Reference numeral 45 represents a coordinate transformation andresolution computer to be described more fully hereinafter whichreceives as inputs at time t = 0 signals proportional to angles A_(z)E_(l), θ, φ, γ, and α_(g) on conductors 39 through 44 respectively whichare connected to stabilized platform 23 by conductors 34 through 38respectively via switch box 29 which serves to pass these signals at andafter time t = 0.

Also at time t = 0 algebraic computer 55, more fully describedhereinbelow, receives as inputs through switch box 29 signalsproportional to the acceleration components of the fighter along therespective i_(o) j_(o) k_(o) inertial coordinate axes. These signalsrepresent or are proportional to V_(F).sup.. k_(o), V_(F).sup.. j_(o),and V_(F).sup.. i_(o), respectively shown on conductors 51, 50, and 49.Algebraic computer 55 also receives signals proportional to α and σ and∫αdt or α which at time t = 0 are representative α_(o) and σ_(o) andα_(o).

By referring to equation 36 the various terms necessary for the solutionfor R_(t) are seen. It may be seen by reference to the above part of thespecification that the V_(F).sup.. i_(o), V_(F).sup.. j_(o), andV_(F).sup.. k_(o) acceleration components are obtained directly from thestabilized platform since at time t = 0 the platform defines theinertial coordinate system i_(o) j_(o) k_(o). Angles θ, φ, α_(g), γ,E_(l) and A_(z) are gimbal and antenna angles and must be resolved intofunctions of α_(t) and σ_(t) by expressing them in terms of the i_(o)j_(o) k_(o) inertial coordinate system.

In the range equation derivation, equations 34 to 36, expressions

    (R.sub.t.sup.. j.sub.o) R.sub.t = cos α.sub.t sin σ.sub.t

    (R.sub.t.sup.. i.sub.o) R.sub.t = cos α.sub.t cos σ.sub.t

    (R.sub.t.sup.. k.sub.o) R.sub.t = -sin α.sub.t

appear. These expressions which appear in the denominator of rangeequation 36 are necessary for the solution of the equation. Angles α_(t)and σ_(t) have previously been defined as α and σ at time t.

The above expression can be stated in matrix form thus:

    __________________________________________________________________________                       R                                                                             | R|                                                    i.sub.o                                                                         cosα.sub.t cosσ.sub.t                                        M =                                                                              j.sub.o                                                                         cosα.sub.t sinσ.sub.t                                           k.sub.o                                                                         -sinα.sub.t                                            which is equivalent to                                                                       R                                                                             | R|                                            cosE.sub.1 cosA.sub.z [cosαcosθcosφ - sinαsin.gam      ma.sinθ - sinαcosγsinφcosθ]                     i.sub.o                                                                         + cosE.sub.1 sinA.sub.z [cosαsinθcosφ + sinαsin.ga      mma.cosθ - sinαcosγsinφsinθ]                      + sinE.sub.1 [cosαsinθ + sinαcosγcosφ]            cosE.sub.1 cosA.sub.z [sinγsinφcosθ - cosγsin.thet      a.]                                                                         j.sub.o                                                                         + cosE.sub.1 sinA.sub.z [cosγcosθ  + sinγsinφsin.t      heta.] - sinE.sub.1 sinγcosφ- cosE.sub.1 cosA.sub.z                 [sinαcosθcosφ + sinγcosαsinθ +              cosαcosγsinφcosθ]-k.sub.o + cosE.sub.1 sinA.sub.z       [sinαsinθcosφ - sinγcosαcosθ  +             cosαcosγsinφsinθ]                                       + sinE.sub.1  [sinαsinφ - cosαcosγcosφ]           __________________________________________________________________________     since both are expressions for R.sub.t in terms of the i.sub.o j.sub.o     k.sub.o coordinate system. The above matrix expression of R.sub.t contains     function of θ, φ, γ, α.sub.g, E.sub.l, and A.sub.z     as can be seen. The signals proportional to these angles are therefore     mathematically manipulated in resolution computer 45 to obtain as outputs     the expressions contained in II so that they may be fed into algebraic     computer 55 which at this point has all the necessary inputs to solve     equation 36.

The manner in which the signals representing angles θ, φ, γ, α_(g),E_(l), and A_(z) are mechanized in resolution computer 45 to providesignals representing the expressions of II will now be discussed inreference to FIG. 4.

Resolver computer 45 receives signals proportional to E_(l), A_(z), θ,φ, γ, and α_(g) which are coupled into resolver units 61, 62, 63, 64,65, 66, respectively, as shown in FIG. 4, which have the function ofobtain ##EQU11## in terms of i_(o) j_(o) k_(o), the terms shown intabulation II.

The resolvers used are of the a.c. type, shown in FIG. 6, in which theinputs are fed in on terminals S₁ and S₂ and the outputs are deliveredon terminals R₁ and R₂. The rotor coils r₁ and r₂ are rotated an amountproportional to a shaft input which in this case is proportional to anangle. If the resolver shown in FIG. 6 has S₁ and S₂ as inputs. Theoutputs are of the form:

    R.sub.1 = S.sub.1 cosA.sub.z + S.sub.2 sin A.sub.z

    R.sub.2 = -S.sub.1 sinA.sub.z - S.sub.2 cos A.sub.z

where A_(z) is the angle through which the rotors r₁ and r₂ are rotated.

Taking resolver 62 of FIG. 5 as an illustrative example of the manner inwhich the resolver computer operates, S₁ = 0 and S₂ = cosE_(l).Therefore, the outputs at R₁ and R₂ are:

    R.sub.1 = cosE.sub.1 sinA.sub.z

    R.sub.2 = cosE.sub.l cosA.sub.z

R₁ and R₂ become the inputs to resolver 63 at S₂ and S₁ respectively.

The remaining resolvers 63 through 66 operate in a manner similar tothat of resolver 62. The output signals from each successive resolverare as shown in FIG. 4. The resulting output signals at terminals 68,69, and 67 are then representative of R in terms of the i_(o) j_(o)k_(o) axes as shown in tabulation II and are in the form necessary toserve as inputs to algebraic computer 55.

It is again noted that the matrix expression of ##EQU12## in terms ofthe i_(o) j_(o) k_(o) as shown in tabulation II is the mathematicalequivalent to that of tabulation I.

The foregoing discussion of FIGS. 3 and 4 has presented an embodiment ofthe invention to the point where all the parameters α, σ, α, V_(F).sup..i_(o), V_(F).sup.. j_(o), V_(F).sup.. k_(o), cos α_(t) cos σ_(t), cosα_(t) sin σ_(t), -sin α_(t) are obtained and ready to be mathematicallymanipulated to solve range equation 36.

FIG. 5 shows algebraic computer 55 in more detail and illustrates amethod by which range equation 36 may be mechanized.

The acceleration components V_(F).sup.. i_(o), V_(F).sup.. j_(o), andV_(F).sup.. k_(o) are inserted into computer 55 where each is integratedtwice by integrators 58, 59, and 60. The output from integrator 58 isconnected via line 52 to tangent function generator and multiplier 72.The output from integrator 59 is connected via line 53 to reciprocalcosine square function generator and multiplier 71. The output fromintegrator 60 is connected via conductor 54 to adder 80. The outputs cosα_(t) sin σ_(t), cos α_(t) cos σ_(t), -sin α_(t) from resolver computer45 are directly connected to reciprocal cosine square function generatorand multiplier 73, tangent function generator and multiplier 74, andadder 75, respectively.

Servo loop 56 has an input representing α driving the mechanicalelements of function generators 71, 72, 73, and 74. At time t = 0 thisinput becomes a constant value represented by α_(o). Servo loops 57 and58 are similar to servo loop 56 and function to insert values of α andσ, which at time t = 0 become α_(o) and σ_(o), into function generatorand multipliers 76, 77, 78, and 79, respectively.

The output from integrator 59 is multiplied by each of the functionscontained in function generators 71, 77, and 78 and the final product isfed into adder 81 on conductor 85. The output from integrator 58 ismultiplied by the function contained in function generator 72 and thisproduct is fed into adder 80 on conductor 86. The output of integrator60 is fed directly into the adder 80 by conductor 54. The output fromadder 80 is added to the output from function generator 78 in adder 81and the output from adder 81 is fed into divider 82 on conductor 91 toprovide a signal proportional to numerator of equation 36.

A signal representing the product tan α_(o) cos α_(t) cos σ_(t), formedin function generator and multiplier 74, is added to a signalrepresenting -sin α in adder 75, the output of which is fed to negativeadder 92 on conductor 89. When the signal representing cos α_(t) sinσ_(t) passes through each of function generator and multipliers 73, 76,and 79 the final output on conductor 90 is a signal representing thequantity ##EQU13## which is an input to negative adder 92.

The output from negative adder 92 is converted as a mechanical input todivider 82 by servo loop 93 where it serves as the denominator ofequation 33. The output of divider 82 is then a voltage representing therange given by equation 36.

The passive ranging system of this invention has been developed toenable it to be easily incorporated into a fighter already equipped witha stabilized platform and a passive type search and track radar system.

Various other modifications of the present invention are possible in thelight of the above teachings. It is therefore to be understood thatwithin the scope of the appended claims, the invention may be practicedotherwise than as specifically described.

What is claimed is:
 1. A passive ranging system for use by a fighter indetermining the distance along the line of sight between the fighter anda target travelling at constant speed; comprising in combination: asearch and track system operable to generate signals proportional to theazimuth and elevation angles of the line of sight with respect to thefighter coordinate system, a stabilized platform normally slaved to saidsearch and track system operable to generate signals proportional to theangular rate of rotation of the line of sight and signals proportionalto the acceleration of the fighter in inertial space, resolver computermeans coupled to said stabilized platform operable to resolve saidangular rate and acceleration signals into terms of a referencecoordinate system, algebraic computer means connected to said stabilizedplatform and said resolver computer operable to transform said signalsinto a voltage form representative of range between the fighter and thetarget.
 2. A system carried by a fighter for passively determining rangebetween the fighter and a radiation emitting target travelling at aconstant velocity, comprising in combination: a search and track antennasystem operable to generate signals proportional to the azimuth andelevation angles of the line of sight to the target with respect to thecoordinate system of the fighter, a stabilized platform for defining aninertial reference coordinate system, said stabilized platform beingslaved to said search and track system and responsive to said azimuthand elevation signals to determine and generate signals proportional toangular and angular rate deviations of the line of sight from saidinertial reference system, said stabilized platform including means forgenerating signals proportional to fighter acceleration components alongthe axes of said inertial reference system, resolver means connected tosaid stabilized platform operable to transform said angular and angularrate signals and said acceleration component signals into terms of saidinertial reference coordinate system, means coupled to said resolveroperable to determine and display the range between said fighter andsaid target.
 3. A passive ranging system carried by a fighter fordetermining the distance along the line of sight between the fighter anda radiation emitting target travelling at a constant velocity;comprising in combination: a radiation sensitive search and track systemoperable to continuously generate signals proportional to azimuth andelevation angles of the target relative to the fighter, a stabilizedplatform normally slaved to said search and track system and defining ageneral coordinate reference system herein designated i j k, saidstabilized platform operable to generate signals proportional to fighteracceleration components along the i j k axes, said said stabilizedplatform operable to generate signals proportional to the angle betweenthe line of sight and the horizontal plane defined by the i j plane, theangular rotation rate of the line of sight about the j axis, and theangular rotation rate of the line of sight about the k axis, a memorydevice coupled to said stabilized platform for receiving said angle andangular rotation rate signals generated by said stabilized platform asinputs thereto operable to store said angle and angular rotation ratesignals at time t = 0, means for connecting said azimuth and elevationangle signals to said stabilized platform, switch means fordisconnecting said azimuth and elevation angle signals from saidstabilized platform at time t = 0 to establish and maintain an inertialcoordinate reference system herein designated i_(o) j_(o) k_(o) wherebysaid stabilized platform generates gimbal angle signals proportional tofighter rotation about said inertial coordinate reference system, aresolution computer connected to said stabilized platform and saidsearch and track system operable to transform said signals proportionalto said gimbal angles and said azimuth and elevation angles in terms ofsaid inertial coordinate reference system, algebraic computer meanscoupled to said resolver computer and said stabilized platform arrangedto receive said stored angle and angular rotation rate signals,acceleration component signals along the axes of the inertial coordinatereference system and said transformed signals proportional to gimbal,azimuth and elevation whereby said algebraic computer determines saiddistance between the fighter and target.
 4. A passive ranging system foruse by a fighter in determining the distance along the line of sightbetween the fighter and a radiation emitting target travelling at aconstant velocity; comprising in combination: a search and track systemoperable to generate signals proportional to the azimuth and elevationangle of the line of sight to the target with respect to the fighter, astabilized platform establishing a reference coordinate system hereindesignated i j k normally slaved to said search and track systemoperable to generate signals proportional to the angle between the lineof sight and the i, j plane, the rotation rate of the line of sightabout the j axis, the rotation rate of the line of sight about the kaxis, means for disconnecting said search and track system from saidstabilized platform at time t = 0 to establish within said stabilizedplatform a fixed inertial reference system herein designated i_(o) j_(o)k_(o), said stabilized platform at time t = 0 and thereafter operable togenerate signals proportional to only fighter rotation about saidinertial reference coordinate system and acceleration components of thefighter along the i_(o) j_(o) k_(o), memory means coupled to saidstabilized platform for storing said angle and rotation rate signals attime t = 0, resolver computer means coupled to said stabilized platformand said search and track system operable to resolve said signalsproportional to azimuth and elevation angles and said signalsproportional to fighter rotation about said inertial referencecoordinate into signals proportional to the angular position of the lineof sight in terms of the inertial coordinate reference system, algebraiccomputer means coupled to said stabilized platform and said resolvercomputer receiving as inputs said stored angle and rotation ratesignals, said signals proportional to acceleration components of thefighter along said inertial reference coordinate system axes, and saidsignals proportional to the angular position of the line of sight interms of the inertial coordinate reference system, said algebraiccomputer operable to determine the range between the fighter and thetarget.
 5. A passive ranging system for use by a fighter in computingdistance along the line of sight from the fighter to a target travellingat constant velocity; comprising in combination: a search and tracksystem operable to generate signals proportional to azimuth andelevation angles of the target with respect to the fighter, a stabilizedplatform slaved to said search and track system operable to continuouslygenerate signals proportional to the angles subtended by the line ofsight with respect to the coordinate system herein designated by i j kof the stabilized platform, said stabilized platform operable togenerate signals proportional to fighter acceleration components alongthe axes of said coordinate system, resolver means coupled to saidstabilized platform operable to transform said signals proportional tofighter acceleration components in terms of the coordinate systemdefined by said stabilized platform at time t = 0, computer meansconnected to said stabilized platform and said resolver computer meansto receive as input the signals proportional to the angles subtended bythe line of sight and said transformed signals proportional to fighteracceleration components whereby said computer determines the distancealong the line of sight from fighter to target.
 6. A passive rangingsystem for use with a fighter in determining the distance along the lineof sight between the fighter and a radiation emitting targer travellinga constant velocity, comprising in combination: a search and tracksystem operable to generate signals proportional to E_(L) and A_(z),where E_(L) is the elevation angle of the line of sight to the targetwith respect to the fighter and A_(z) is the azimuth angle of the lineof sight to the target with respect to the fighter; a stabilizedplatform of the type having four gimbals establishing a referencecoordinate system herein designated i j k normally slaved to said searchand track system operable to generate signals proportional to α, α andσ, where α equals the angle between the line of sight and the planedefined by the i j axis, α equals the rotation rate of the line of sightabout the j axis, and σ equals the rotation rate of the line of sightabout the k axis; means for disconnecting said search and track systemfrom said stabilized platform at time t = 0 to establish within saidstabilized platform a fixed inertial reference system, herein designatedi_(o) j_(o) k_(o) ; said stabilized platform at time t = 0 andthereafter operable to generate signals proportional to the gimbalangles φ, θ, γ, and α_(g) where θ equals platform azimuth angle(displacement about k_(o) axis), φ equals platform elevation angle(displacement about j_(o) axis), γ equals platform roll angle(displacement about i_(o) axis), α_(g) equals platform inner pitch anglewhich describe fighter rotation about said inertial reference coordinatesystem; said stabilized platform also operable to generate signalsproportional to acceleration components of the fighter along the i_(o)j_(o) k_(o) axes where V_(F).sup.. i_(o) equals fighter accelerationalong the i axis, V_(F).sup.. j_(o) equals fighter acceleration alongthe j_(o) axis; and V_(F).sup.. k_(o) equals fighter acceleration alongthe k_(o) axis; memory means coupled to said stabilized platform forstoring α, α and σ signals at time t = 0, at which time α becomes α_(o),α becomes α_(o) and σ becomes σ_(o) ; resolver computer means coupled tosaid stabilized platform and said search and track system operable toresolve said signals proportional to E, A, θ, φ, γ, and α_(g) intosignals indicative of the angular position of the line of sight in termsof the inertial coordinate reference system at time t = t, which are cosα_(t) cos σ_(t), cos α_(t) sin σ_(t), and - sin α_(t) which areexpressions for range vector taken along the i_(o) j_(o) k_(o) axesrespectively at time t = t where α = α_(t) at time t = t and where σ =σ_(t) at time t = t; algebraic computer means coupled to said stabilizedplatform and said resolver computer receiving as inputs said storedangle and rotation rate signals α_(o), α_(o), σ_(o), said accelerationcomponent signals V_(F).sup.. i_(o), V_(F).sup.. j_(o), V_(F).sup..k_(o), cos α_(t) cos σ_(t), cos α_(t) sin σ_(t), and - sin α_(t),whereby said algebraic computer transforms and combines these inputsinto a voltage representative of the range equation: ##EQU14##
 7. Amethod for passively determining the range along the line of sightbetween a fighter and a target travelling at constant velocity,comprising the steps of: determining the azimuth and elevation angles ofthe line of sight with repect to the fighter coordinate system,determining the angular rate of rotation of the fighter about aninertial coordinate reference system, determining fighter accelerationwith respect to inertial space, resolving said azimuth, elevation, androtation rate angles into angular quantities representative of theposition of the line of sight with respect to said inertial coordinatesystem, and determining from said angular quantities and saidacceleration the range along the line of sight from fighter to target.